Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![nereasing and decr
5. f(x) = (x2-9)2/3
a. Find the domain.
Domain: R = (-00,)
b. Find the x-intercept(s) and the y-intercept, if any.
y-f(x) =0 (X- 9)3 -0
y =(81)"3 =
33 =33)'3
x²-9=0
X-intercepts
(3,0) 63,0)
y-intercapt is (0,335)20, 4.3267)
メ=9
xニ±3]
c. Find any symmetry in the graph.
y=-y=)-y=(x²-9)*
2/3
no symmetry about x-axis because its
not
equivelent to onginal
function.
Xニ-x リ=(x)-9)~
about
symmetry
y=(x²-9)"3 equivalent to original function.
y-axıs beceuse its
18ymmetry:
= About
y-axıs
d. Find the end behavior of the graph and find all vertical, horizontal, or slant asymptotes.
Vertical Asymptote: There are no such point in the function flx)
where the domominator of function equa's zero
or DNE
Thus, no vertical asymptote.
Horizontal Asupptobe; f)=
Iim
Thus, there is no homi 2ontal asymptote
Blent Asumptoteiy=mx+bis slant asymptote of function if
=0 or
1213.
Thus, there is no slant asymptote](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae7a862e-0ee1-4a84-a4fd-63344cf59edd%2Fdd7847d7-5aff-453a-a6fc-5164b34d2c58%2F38ubvp4_processed.jpeg&w=3840&q=75)
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